Problem: What do the following two equations represent? $2x-y = 4$ $3x+6y = -5$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x-y = 4$ $-y = -2x+4$ $y = 2x - 4$ Putting the second equation in $y = mx + b$ form gives: $3x+6y = -5$ $6y = -3x-5$ $y = -\dfrac{1}{2}x - \dfrac{5}{6}$ The slopes are negative inverses of each other, so the lines are perpendicular.